Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁ = 5 -5 4₂5 2 2 -1 U3 = **** OA. U₁-25 ₂ = u₁-u3 = 4₂-43 = 1 1 4 + Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R? Select all that apply. and x = A. The vectors must span W. B. The vectors must form an orthogonal set. C. The vectors must all have a length of 1. D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? OA. IfS={U₁. up) and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. OB. If S= (u₁... up) and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set.. OC. If S= (₁. Up}! is a basis in RP, then the members of S span RP and hence form an orthogonal set. OD. If S = (u₁.... up) is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. Which calculations should be performed next? (Simplify your answers.) Vis 5 -2 How do these calculations show that (u₁, U₂, U3} is an orthogonal basis for R³? Since each the vectors Express x as a linear combination of the u's. x= (Use integers or fractions for any numbers in the equation.) OB. From the theorem above, this proves that the vectors are also 4₁4₂ UU U₂U3 =
Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁ = 5 -5 4₂5 2 2 -1 U3 = **** OA. U₁-25 ₂ = u₁-u3 = 4₂-43 = 1 1 4 + Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R? Select all that apply. and x = A. The vectors must span W. B. The vectors must form an orthogonal set. C. The vectors must all have a length of 1. D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? OA. IfS={U₁. up) and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. OB. If S= (u₁... up) and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set.. OC. If S= (₁. Up}! is a basis in RP, then the members of S span RP and hence form an orthogonal set. OD. If S = (u₁.... up) is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. Which calculations should be performed next? (Simplify your answers.) Vis 5 -2 How do these calculations show that (u₁, U₂, U3} is an orthogonal basis for R³? Since each the vectors Express x as a linear combination of the u's. x= (Use integers or fractions for any numbers in the equation.) OB. From the theorem above, this proves that the vectors are also 4₁4₂ UU U₂U3 =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 38EQ
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